You're supposed to rinse the media in siphoned water, but don't throw it away.

If you clean the filter media once a month, it wouldn't be that GROSS.

If you only rinse the media once every 3 months it'll get nastier.

What brand & model filter is it?

What size tank do you have?

What kind of fish live inside?

I use filter floss in combination with carbon/zeolite. I dump the filter floss when it's completely black. But after what I've learned on this forum, I'm just going to give it a good rinsing in the siphoned water to remove the chunks.

Carbon is not poisonous to the fish but don't dump out the carbon into the tank. It should stay in the filter.

Also the used carbon can be mixed in with your garden soil to be used as fertilizer for your trees and flowers.

Oh dear, it sounds like you may have lost the cycle :/
Bacteria thrive on the filter media, and by throwing away the carbon filter, you've almost certainly lost a good portion of beneficial bacteria.
I'd say to watch your parameters closely the next few days. There's probably enough bacteria in your substrate to start a new cycle.
Next time, just swish the filter media around in old tank water (NEVER hot or tap water) to clean it out. I'd only replace it if you noticed a change in the filter's flow.

It's ok, we all make mistakes
That's how I destroyed the already unstable cycle in my 3-gal /)__-